We can translate the statement of Theorem REF  into an adjoint equivalence in the
orbifold completion \({B}_{\textsf {\tiny YM}}^\mathrm {orb}\)  [1]} of the topological
defect bicategory of two-dimensional Yang-Mills theories
\({B}_{\textsf {\tiny YM}}\) , which is idempotent complete by
Proposition REF . Since the objects of
\({B}_{\textsf {\tiny YM}}\)  are bimodules in the symmetric monoidal
category \({{H}\mathsf {ilb}}\) , and the left and right duality morphisms can be
related by the symmetric braiding, it follows that the defect
bicategory \({B}_{\textsf {\tiny YM}}\)  is pivotal, similarly to the
case of topological field theories.
